invest_3ed.pdf

# 460 df 3 p value 0000 this procedure is valid because

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Chi-Sq = 84.460, DF = 3, P-Value = 0.000 This procedure is valid because all of the expected counts are far larger than 5, and we are assuming that the Pew organization took independent random samples across the regions. Their report mentions that they used random digit dialing with extensive follow- up efforts, but it’s not clear whether they took independent samples within these regions or took a nationwide sample and treated region as one of the variables. Either way the chi-square analysis is valid. The p-value is extremely small (0.000 to three decimal places), indicating that the differences observed in the sample proportions would almost never occur by chance if the population proportions were really equal across the four regions. Thus, we have overwhelming evidence to reject the null hypothesis and conclude that the proportions of internet users are not the same in these four regions. In an effort to say a little bit more, we can examine the cell contributions. We see that the largest contributions occur in the West and South. The West had more internet users, 3259, (and so fewer non- internet users) than would have been expected if the proportions were all the same, 3042.05, and the South had fewer internet users, 2372, (and so more non-users) than would have been expected, 1766.66. The observed counts in the Northeast and Midwest regions were fairly close to the expected counts. In conclusion, the sample data provide very strong evidence that the population proportions of internet users differ across regions of the United States. The differences in the sample proportions are larger than can reasonably be explained by random sampling variation. The large sample sizes in this study help to render the differences among the samples statistically significant even though the sample proportions seem to be fairly similar in practical terms.

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Chance/Rossman, 2015 ISCAM III Example 5.2 407 Example 5.2: Lifetimes of Notables The 1991 World Almanac and Book of Facts contained a section on “noted personalities” in a total of nine occupational categories. The lifetimes of these people can be found in the lifetimesFull.txt data file. Analyze these data to address the question of whether the average lifetimes across these occupational categories differ significantly. Include graphical and numerical summaries as well as a test of significance. Summarize your conclusions.
Chance/Rossman, 2015 ISCAM III Example 5.2 408 Analysis To compare several groups on a quantitative variable, we will consider analysis of variance. The first step will be to describe the data we have. The file lifetimesFull contains the lifetimes (years) of notable personalities from nine different occupation classifications. The samples were selected independently from within each job classification but they were presumably not selected at random.

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